Time-series analysis of transient chaos.

Abstract

A time-series analysis method of transient chaos is worked out which can also be applied to signals of laboratory experiments. The process is based on the construction of a long artificial time series obtained by gluing pieces of many transiently chaotic signals together. This artificial signal represents a long-time motion in the vicinity of the nonattracting chaotic set. Thus all of the well-known numerical methods developed for analyzing permanent chaotic behavior are applicable in a more convenient way than using many short separated time-series pieces. The method is illustrated and its validity is checked by the H\'enon map. The nonattracting strange set is reconstructed in the presence of both a periodic and a chaotic attractor, and quantitative characteristics such as dimensions and Lyapunov exponents are determined by means of time-delay embedding methods.